Question

Cristine's middle school has a total of 900 students and 45 teachers. The local high school has 110 teachers and a student-teacher ratio proportional to the middle school's. How many students will Cristine find when she gets to high school? A) 900 B) 1100 C) 2200 D) 2500

Answer 1

Write and solve an equation of ratios:

900 students      45 teachers         
------------------  = -----------------  
          x               110 teachers     

Cross multiplying, we get (900)(110) / 45, or

                                                                 
so x = # of students in the high school = 2200   (answer)
                                                                    

Answer 2

Answer:

Option C. 2200 is correct

Step-by-step explanation:

Number of teachers in middle school = 45

Number of students in middle school = 900

$\text{Ratio of students to teacher in middle school = }\frac{900}{45}$

Number of teachers in Local high school = 110

Let number of students in local high school = x

$\text{Ratio of students to teacher in local high school = }\frac{x}{110}$

But, according too the question, both the ratios are given proportional to each other.

⇒ Ratio of students to teacher in middle school = Ratio of students to teacher in local high school

$\implies \frac{900}{45}=\frac{x}{110}\\\\\implies x=\frac{110\times 900}{45}\\\\\implies x = 2200$

Hence, number of students required in the local high school = 2200

Therefore, Option C. 2200 is correct